This paper reports part of the activities in progress in our laboratory in the investigation of electrode and electrolyte materials which may be of interest for the development of lithium-ion batteries with improved characteristics and performances. This investigation has been directed to both anode and cathode materials, with particular attention to convertible oxides and defect spinel-framework Li-insertion compounds in the anode area and layered mixed lithium-nickel-cobalt oxide and high voltage, metal type oxides in the cathode area. As for the electrolyte materials, we have concentrated the efforts on composite polymer electrolytes and gel-type membranes. In this work we report the physical, chemical and electrochemical properties of the defect spinel-framework Li-insertion anodes and of the high voltage, mixed metal type oxide cathodes, by describing their electrochemical properties in cells using either "standard" liquid electrolytes and "advanced" gel-type, polymer electrolytes. The results illustrated here demonstrate that the spinel-framework anodes of the Li[Li1/3Ti5/3]O-4 type can be combined with high voltage cathodes of the Li2Mn(4-x)O8 family for the fabrication of new types of lithium-ion battery systems cycling around 3.5 V. The development of this interesting concept is however still limited by the availability of highly stable electrolytes.